A dimension reduction method for fast diffuse optical tomography

Abstract

Because the inverse problem in diffuse optical tomography (DOT) is highly ill-posed in general, appropriate regularization based on prior knowledge of the target is necessary for the reconstruction of the image. The total variation L1 norm regularization method (TV-L1) that preserves the boundaries of a target is known to have excellent result in image reconstruction. However, large computational cost of the TV-L1 prevents its use in portable applications. In this study, we propose a dimension reduction method in DOT for fast and hardware-efficient image reconstruction. The proposed method is based on the fact that the optical flux from a light source in a highly scattering medium is localized spatially. As such, the dimension of a sensitivity matrix used in the forward model of the DOT can be reduced by eliminating uncorrelated subspaces. The simulation results indicate up to 96.1% reduction in dimensions and up to 79.3% reduction in runtime while suppressing the reconstruction error below 2.26%.